Hesitant-Intuitionistic Trapezoidal Fuzzy Prioritized Operators Based on Einstein Operations with Their Application to Multi-criteria Group Decision-Making

Sarkar, Arun; Biswas, Animesh

doi:10.1007/978-981-15-1041-0_1

Cited by 3 publications

(3 citation statements)

References 33 publications

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“…Step 2. To aggregate all the individual normalized decision matrices,R (1) ,R (2) , andR (3) into a collective DHq-ROFDM,R , with associated weight vector, w = (0.35,0.40,0.25) T , utilize DHq-ROFWDBM operator, as presented in Equation (23). The resultant DHq-ROFDM,R is presented below.…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…In PF environments, Prof. R. R. Yager 7,8 introduced weighted averaging (WA) and weighted geometric (WG) AOs, namely, PFWA, PFWG, weighted PF power average and weighted PF power geometric AOs by extending the concept of AOs under fuzzy and IF domains. [20][21][22][23][24] Peng and Yuan 25 introduced generalized PFWA and generalized PF point AOs. In most of the above mentioned cases biasness of using membership and nonmembership degrees are observed under PF contexts.…”

Section: Introductionmentioning

confidence: 99%

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Dual hesitant q ‐rung orthopair fuzzy Dombi t ‐conorm and t ‐norm based Bonferroni mean operators for solving multicriteria group decision making problems

Sarkar

Biswas

2021

Int J Intell Syst

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In this paper, Bonferroni mean (BM) and Dombi t-conorms and t-norms (Dt-CN&t-Ns) are combined under dual hesitant q-rung orthopair fuzzy (DHq-ROF) environment to produce DHq-ROF-Dombi BM, weighted Dombi BM, Dombi geometric BM, and Dombi weighted geometric BM aggregation operators (AOs). Using these operators, the decision making processes would become more flexible and also would possess the capabilities of capturing interrelationships among input arguments under imprecise decision making environments. Apart from those, a large number of AOs either already developed or not yet developed may also be derived from the proposed AOs. In the process of developing the AOs, some operational laws of DHq-ROF numbers based on Dt-CN&t-Ns are defined first. Several important properties of the developed operators are discussed. The proposed AOs are used to frame a new methodology to solve multicriteria group decision making problems under DHq-ROF contexts. Several illustrative examples are solved to demonstrate effectiveness and benefits of the developed method. Sensitivity analysis is performed to show the variations of ranking values with the change of different parameters in the decision making contexts. Finally, the introduced method is compared with several existing techniques to establish superiority and effectiveness of the proposed method.

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Section: Illustrative Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dual hesitant q ‐rung orthopair fuzzy Dombi t ‐conorm and t ‐norm based Bonferroni mean operators for solving multicriteria group decision making problems

Sarkar

Biswas

2021

Int J Intell Syst

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“…Under this situation, Atanassov (1986) extended FSs to intuitionistic fuzzy (IF) sets (IFSs) by assigning membership degree along with non‐membership degree for the elements of universe of discourse, satisfying the condition that the sum of those degrees is less or equals to 1. Several MCDM processes in IF environment (Biswas & Debnath, 2018; Kumar & Biswas, 2019; Sarkar & Biswas, 2020a) are found in the literature. Afterwards, Yager (2013, 2014) introduced Pythagorean fuzzy (PF) sets (PFSs) as an extension of IFSs.…”

Section: Introductionmentioning

confidence: 99%

A multi‐criteria decision making approach for strategy formulation using Pythagorean fuzzy logic

Sarkar¹,

Biswas

2021

Expert Systems

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The objective of this paper is to develop Pythagorean fuzzy (PF) multi‐objective optimization by ratio analysis (PF‐MOORA) plus full MULTIplicative form (PF‐MULTIMOORA) method for solving multicriteria decision making (MCDM) problems with completely unknown information of criteria weights. In the model formulation process, a new distance measure is defined to quantify the difference between PF sets by combining Hamming distance and Hausdorff metric. This distance measure is, subsequently, implemented in entropy weight model for determining unknown weights of criteria, and also in reference point approach for obtaining preference indices of alternatives. To overcome the deficiencies occurred in existing MULTIMOORA method, like multiple comparisons, circular reasoning, and so on, an aggregation‐based approach is recommended in the proposed PF‐MULTIMOORA. To demonstrate the feasibility and practicality of the proposed method, an example concerning strategy prioritization of a tiles manufacturing company is presented. In the strategy evaluation process, at first, the judgement values provided by the decision maker are expressed in linguistic terms, and then those are converted into PF numbers through a PF weighting scale. The sensitivity of the proposed model is validated by changing of weights of criteria which impact on the ranks of the strategies. To show robustness of the developed method, the result attained by applying PF‐MULTIMOORA is compared with existing techniques, not only in crisp and fuzzy quantitative strategic planning matrix context, but also using four other MCDM methods, namely, modified PF‐MOORA, as a particular case of the proposed PF‐MULTIMOORA technique, PF weighted sum, PF‐TOPSIS and PF‐VIKOR.

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Multi-criteria group decision making through full multiplicative form under hesitant Fermatean fuzzy environment

Luqman,

Siddique,

Shahzadi

et al. 2024

Granul. Comput.

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Hesitant-Intuitionistic Trapezoidal Fuzzy Prioritized Operators Based on Einstein Operations with Their Application to Multi-criteria Group Decision-Making

Cited by 3 publications

References 33 publications

Dual hesitant q ‐rung orthopair fuzzy Dombi t ‐conorm and t ‐norm based Bonferroni mean operators for solving multicriteria group decision making problems

Dual hesitant q ‐rung orthopair fuzzy Dombi t ‐conorm and t ‐norm based Bonferroni mean operators for solving multicriteria group decision making problems

A multi‐criteria decision making approach for strategy formulation using Pythagorean fuzzy logic

Multi-criteria group decision making through full multiplicative form under hesitant Fermatean fuzzy environment

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